A light-emitting device includes a compound semiconductor having a characteristic of converting electrical energy into light energy. The light-emitting device may include compound semiconductors belonging to group III and V on the periodic table. The light-emitting device can represent various colors hv adjusting the compositional ratio of the compound semiconductors.
When forward voltage is applied to the light-emitting device, electrons of an N layer are combined with holes of a P layer, so that energy may be diverged corresponding to an energy gap between a conduction band and a valance band. The energy is mainly emitted in the form of heat or light, In the case of the light-emitting device, the energy is diverged in the form of light.
For example, a nitride semiconductor represents superior thermal stability and wide bandgap energy so that the nitride semiconductor has been spotlighted in the field of optical devices and high-power electronic devices. In particular, blue, green, and ultraviolet (UV) light-emitting devices employing the nitride semiconductor have already been commercialized and extensively used.
FIG. 1 is a view showing an energy band for an active layer of a light-emitting device according to the related art, and FIG, 2 is an energy band diagram obtained by simulating the active layer of the light-emitting device shown in FIG. 1.
Referring to FIGS. 1 and 2, according to the related art, the active layer may include a plurality of quantum well layers 20a and a plurality of quantum barrier layers 20b. The quantum well layers 20a and the quantum barrier layers 20b may be formed of a semiconductor compound such as InGaN/InGaN.
In general, the energy band of the active layer is divided into a conductive band and a valence band. A conductive band energy level Ec and a valance band energy level Ev are formed while facing each other and have lower values in the quantum well layers 20a and higher values in the quantum barrier layers 20b. 
As shown in the drawing, the conductive band energy level Ec and the valance band energy level Ev in the active layer substantially have energy band waveforms as shown in dotted lines (--). The energy band waveforms are determined by wave functions fc and fv of holes and electrons, which are determined in the quantum well layer 20a and the quantum barrier layer 20b, respectively.
However, a strong piezoelectric field is formed in the quantum well layer 20a formed of InGaN due to the stress resulting from an asymmetry and a lattice constant mismatch of a Wurzite structure and. The strong piezoelectric field biases the wave functions fc and fv of holes and electrons to significantly reduce transition probability.
As shown in drawings, the wave functions fc and fv of the conductive band and the valance band facing the conductive band in the quantum well layer 20a of the active layer are biased to the quantum barrier layer 20b (regions X and X′ are biased in directions opposite to each other).
In an enlarged view of a region A of FIG. 2, the region X of the wave funcation fc at the conductive band and the region X′ of the wave function fv at the valance band are not mismatched with each other in a vertical direction and biased to right and left sides, respectively.
As the wave functions fc and fv are biased, the energy band waveform Ec at the conductive band and the energy band waveform Ev at the valance band are based to space electrons and holes collected in the quantum well layer 20a away from each other (regions Y and Y′ are biased in the directions opposite to each other).
In particular, square roots of absolute values of wave functions fc and fv in the quantum well layer are expressed as |fc|2 and |fv|2, respectively, which refer to probability density functions of holes and electrons ire the quantum well layer, respectively. The probability density functions refer to densities at which the electrons and the holes exist in the conductive band and the valance band, respectively. The regions having the highest probability density are spaced apart from each other to reduce transition probability (coupling probability) of holes and electrons, so that internal quantum efficiency (IQE) is degraded.